diff --git a/src/pip/_internal/resolution/resolvelib/resolver.py b/src/pip/_internal/resolution/resolvelib/resolver.py
index cba5a496508..5ec4a97b6a7 100644
--- a/src/pip/_internal/resolution/resolvelib/resolver.py
+++ b/src/pip/_internal/resolution/resolvelib/resolver.py
@@ -15,9 +15,10 @@
 from .factory import Factory
 
 if MYPY_CHECK_RUNNING:
-    from typing import Dict, List, Optional, Tuple
+    from typing import Dict, List, Optional, Set, Tuple
 
     from pip._vendor.resolvelib.resolvers import Result
+    from pip._vendor.resolvelib.structs import Graph
 
     from pip._internal.cache import WheelCache
     from pip._internal.index.package_finder import PackageFinder
@@ -114,42 +115,21 @@ def resolve(self, root_reqs, check_supported_wheels):
 
     def get_installation_order(self, req_set):
         # type: (RequirementSet) -> List[InstallRequirement]
-        """Create a list that orders given requirements for installation.
+        """Get order for installation of requirements in RequirementSet.
 
-        The returned list should contain all requirements in ``req_set``,
-        so the caller can loop through it and have a requirement installed
-        before the requiring thing.
+        The returned list contains a requirement before another that depends on
+        it. This helps ensure that the environment is kept consistent as they
+        get installed one-by-one.
 
-        The current implementation walks the resolved dependency graph, and
-        make sure every node has a greater "weight" than all its parents.
+        The current implementation creates a topological ordering of the
+        dependency graph, while breaking any cycles in the graph at arbitrary
+        points. We make no guarantees about where the cycle would be broken,
+        other than they would be broken.
         """
         assert self._result is not None, "must call resolve() first"
-        weights = {}  # type: Dict[Optional[str], int]
 
         graph = self._result.graph
-        key_count = len(self._result.mapping) + 1  # Packages plus sentinal.
-        while len(weights) < key_count:
-            progressed = False
-            for key in graph:
-                if key in weights:
-                    continue
-                parents = list(graph.iter_parents(key))
-                if not all(p in weights for p in parents):
-                    continue
-                if parents:
-                    weight = max(weights[p] for p in parents) + 1
-                else:
-                    weight = 0
-                weights[key] = weight
-                progressed = True
-
-            # FIXME: This check will fail if there are unbreakable cycles.
-            # Implement something to forcifully break them up to continue.
-            if not progressed:
-                raise InstallationError(
-                    "Could not determine installation order due to cicular "
-                    "dependency."
-                )
+        weights = get_topological_weights(graph)
 
         sorted_items = sorted(
             req_set.requirements.items(),
@@ -159,6 +139,52 @@ def get_installation_order(self, req_set):
         return [ireq for _, ireq in sorted_items]
 
 
+def get_topological_weights(graph):
+    # type: (Graph) -> Dict[Optional[str], int]
+    """Assign weights to each node based on how "deep" they are.
+
+    This implementation may change at any point in the future without prior
+    notice.
+
+    We take the length for the longest path to any node from root, ignoring any
+    paths that contain a single node twice (i.e. cycles). This is done through
+    a depth-first search through the graph, while keeping track of the path to
+    the node.
+
+    Cycles in the graph result would result in node being revisited while also
+    being it's own path. In this case, take no action. This helps ensure we
+    don't get stuck in a cycle.
+
+    When assigning weight, the longer path (i.e. larger length) is preferred.
+    """
+    path = set()  # type: Set[Optional[str]]
+    weights = {}  # type: Dict[Optional[str], int]
+
+    def visit(node):
+        # type: (Optional[str]) -> None
+        if node in path:
+            # We hit a cycle, so we'll break it here.
+            return
+
+        # Time to visit the children!
+        path.add(node)
+        for child in graph.iter_children(node):
+            visit(child)
+        path.remove(node)
+
+        last_known_parent_count = weights.get(node, 0)
+        weights[node] = max(last_known_parent_count, len(path))
+
+    # `None` is guaranteed to be the root node by resolvelib.
+    visit(None)
+
+    # Sanity checks
+    assert weights[None] == 0
+    assert len(weights) == len(graph)
+
+    return weights
+
+
 def _req_set_item_sorter(
     item,     # type: Tuple[str, InstallRequirement]
     weights,  # type: Dict[Optional[str], int]
diff --git a/tests/unit/resolution_resolvelib/test_resolver.py b/tests/unit/resolution_resolvelib/test_resolver.py
index aef80f55e39..6ae6bd7936f 100644
--- a/tests/unit/resolution_resolvelib/test_resolver.py
+++ b/tests/unit/resolution_resolvelib/test_resolver.py
@@ -6,7 +6,10 @@
 
 from pip._internal.req.constructors import install_req_from_line
 from pip._internal.req.req_set import RequirementSet
-from pip._internal.resolution.resolvelib.resolver import Resolver
+from pip._internal.resolution.resolvelib.resolver import (
+    Resolver,
+    get_topological_weights,
+)
 
 
 @pytest.fixture()
@@ -26,6 +29,21 @@ def resolver(preparer, finder):
     return resolver
 
 
+def _make_graph(edges):
+    """Build graph from edge declarations.
+    """
+
+    graph = DirectedGraph()
+    for parent, child in edges:
+        parent = canonicalize_name(parent) if parent else None
+        child = canonicalize_name(child) if child else None
+        for v in (parent, child):
+            if v not in graph:
+                graph.add(v)
+        graph.connect(parent, child)
+    return graph
+
+
 @pytest.mark.parametrize(
     "edges, ordered_reqs",
     [
@@ -40,9 +58,9 @@ def resolver(preparer, finder):
         (
             [
                 (None, "toporequires"),
-                (None, "toporequire2"),
-                (None, "toporequire3"),
-                (None, "toporequire4"),
+                (None, "toporequires2"),
+                (None, "toporequires3"),
+                (None, "toporequires4"),
                 ("toporequires2", "toporequires"),
                 ("toporequires3", "toporequires"),
                 ("toporequires4", "toporequires"),
@@ -59,15 +77,7 @@ def resolver(preparer, finder):
     ],
 )
 def test_new_resolver_get_installation_order(resolver, edges, ordered_reqs):
-    # Build graph from edge declarations.
-    graph = DirectedGraph()
-    for parent, child in edges:
-        parent = canonicalize_name(parent) if parent else None
-        child = canonicalize_name(child) if child else None
-        for v in (parent, child):
-            if v not in graph:
-                graph.add(v)
-        graph.connect(parent, child)
+    graph = _make_graph(edges)
 
     # Mapping values and criteria are not used in test, so we stub them out.
     mapping = {vertex: None for vertex in graph if vertex is not None}
@@ -80,3 +90,147 @@ def test_new_resolver_get_installation_order(resolver, edges, ordered_reqs):
     ireqs = resolver.get_installation_order(reqset)
     req_strs = [str(r.req) for r in ireqs]
     assert req_strs == ordered_reqs
+
+
+@pytest.mark.parametrize(
+    "name, edges, expected_weights",
+    [
+        (
+            # From https://github.com/pypa/pip/pull/8127#discussion_r414564664
+            "deep second edge",
+            [
+                (None, "one"),
+                (None, "two"),
+                ("one", "five"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+            ],
+            {None: 0, "one": 1, "two": 1, "three": 2, "four": 3, "five": 4},
+        ),
+        (
+            "linear",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND root -> two",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                (None, "two"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND root -> three",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                (None, "three"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND root -> four",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                (None, "four"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND root -> five",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                (None, "five"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND one -> four",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                ("one", "four"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND two -> four",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                ("two", "four"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND four -> one (cycle)",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                ("four", "one"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND four -> two (cycle)",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                ("four", "two"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+        (
+            "linear AND four -> three (cycle)",
+            [
+                (None, "one"),
+                ("one", "two"),
+                ("two", "three"),
+                ("three", "four"),
+                ("four", "five"),
+                ("four", "three"),
+            ],
+            {None: 0, "one": 1, "two": 2, "three": 3, "four": 4, "five": 5},
+        ),
+    ],
+)
+def test_new_resolver_topological_weights(name, edges, expected_weights):
+    graph = _make_graph(edges)
+
+    weights = get_topological_weights(graph)
+    assert weights == expected_weights